Discrete time methods for simulating continuous time Markov chains

1976 ◽  
Vol 8 (4) ◽  
pp. 772-788 ◽  
Author(s):  
Arie Hordijk ◽  
Donald L. Iglehart ◽  
Rolf Schassberger
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Confidence Intervals ◽  
Discrete Time ◽  
Continuous Time ◽  
Statistical Efficiency ◽  
Numerical Examples ◽  
The Central Limit Theorem ◽  
Continuous Time Markov Chains

This paper discusses several problems which arise when the regenerative method is used to analyse simulations of Markov chains. The first problem involves calculating the variance constant which appears in the central limit theorem used to obtain confidence intervals. Knowledge of this constant is very helpful in evaluating simulation methodologies. The second problem is to devise a method for simulating continuous time Markov chains without having to generate exponentially distributed holding times. Several methods are presented and compared. Numerical examples are given to illustrate the computional and statistical efficiency of these methods.

Discrete time methods for simulating continuous time Markov chains

1976 ◽  
Vol 8 (04) ◽  
pp. 772-788 ◽  
Author(s):  
Arie Hordijk ◽  
Donald L. Iglehart ◽  
Rolf Schassberger
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Confidence Intervals ◽  
Discrete Time ◽  
Continuous Time ◽  
Statistical Efficiency ◽  
Numerical Examples ◽  
The Central Limit Theorem ◽  
Continuous Time Markov Chains

This paper discusses several problems which arise when the regenerative method is used to analyse simulations of Markov chains. The first problem involves calculating the variance constant which appears in the central limit theorem used to obtain confidence intervals. Knowledge of this constant is very helpful in evaluating simulation methodologies. The second problem is to devise a method for simulating continuous time Markov chains without having to generate exponentially distributed holding times. Several methods are presented and compared. Numerical examples are given to illustrate the computional and statistical efficiency of these methods.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (04) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

Conditions for strong ergodicity using intensity matrices

1988 ◽  
Vol 25 (1) ◽  
pp. 34-42 ◽  
Author(s):  
Jean Johnson ◽  
Dean Isaacson
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Limiting Behavior ◽  
Strong Ergodicity ◽  
Continuous Time Markov Chains

Sufficient conditions for strong ergodicity of discrete-time non-homogeneous Markov chains have been given in several papers. Conditions have been given using the left eigenvectors ψn of Pn(ψ nPn = ψ n) and also using the limiting behavior of Pn. In this paper we consider the analogous results in the case of continuous-time Markov chains where one uses the intensity matrices Q(t) instead of P(s, t). A bound on the rate of convergence of certain strongly ergodic chains is also given.

Statistical Simulation with Web-Based Apps

2018 ◽  
Vol 111 (6) ◽  
pp. 466-469
Author(s):  
Anne Quinn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Confidence Intervals ◽  
Central Limit ◽  
Web Application ◽  
Original Data ◽  
Statistical Simulation ◽  
Web Based ◽  
The Central Limit Theorem

While looking for an inexpensive Web application to illustrate the Central Limit theorem, I found the Rossman/Chance Applet Collection, a group of free Web-based statistics apps. In addition to illustrating the Central Limit theorem, the apps could be used to cover many classic statistics concepts, including confidence intervals, regression, and a virtual version of the popular Reese's® Pieces problem. The apps allow users to investigate concepts using either preprogrammed or original data.

Statistical Inference and Simulation with StatKey

2016 ◽  
Vol 109 (9) ◽  
pp. 708-711 ◽  
Author(s):  
Anne Quinn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Central Limit ◽  
Real Data ◽  
Web Based ◽  
The Central Limit Theorem

StatKey, a free Web-based app, supplies real data to help with the central limit theorem, confidence intervals, and much more.

scholarly journals Subgeometric Ergodicity Analysis of Continuous-Time Markov Chains under Random-Time State-Dependent Lyapunov Drift Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Random Time ◽  
Lyapunov Analysis ◽  
Continuous Time Markov Chains ◽  
State Dependent ◽  
Drift Conditions

We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs). We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.

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